Many Calculators or Computers Cannot Directly Calculate 70 ! or Higher

question 131

Multiple Choice

Many calculators or computers cannot directly calculate 70 ! or higher. When $\mathrm { n }$ is large, $\mathrm { n }$ ! can be approximated by $n ! = 10 \mathrm {~K}$ , where $\mathrm { K } = ( \mathrm { n } + 0.5 ) \log \mathrm { n } + 0.39908993 - 0.43429448 \mathrm { n }$ .
Evaluate 95 ! using the approximation given above.

• A) \(1.059 \times 10 ^ { 147 }\)
• B) \(1.032 \times 10 ^ { 148 }\)
• C) \(1.087 \times 10 ^ { 394 }\)
• D) \(1.480 \times 10 ^ { 2 }\)

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Definitions:

Discretionary Income

Discretionary income is the amount of an individual's income left for spending, investing, or saving after taxes and personal necessities (like food and shelter) have been paid.

Positively Correlated

A relationship between two variables where an increase in one variable is associated with an increase in the other.

Scientific Method

A systematic, organized series of steps that helps ensure objectivity and consistency in exploring a social or scientific question.

Inductive Reasoning

A logical process in which multiple premises, all believed true or found true most of the time, are combined to obtain a specific conclusion.